I'm using a Twinview-Setup, the left screen is for watching TV and videos only, the right one is for normal working. So I defined the right screen as the primary screen. KDE is putting Plasma on the right screen, so this seems to work, but all new windows are opened on the left screen, and I have to move them to the right one every time. Is there a solution to force all windows to appear on the right (primary) screen?

The driver has no control over where windows get placed, that's up to the window manager. The driver can provide hints; see the TwinViewXineramaInfoOrder option for example, but ultimately it is the window manager that decides where windows should be placed. I would suggest contacting KDE's support forums.